and the vacuum energy \(\rho _\Lambda \)  comparable to our current critical energy density. The related idea was discussed in Ref. [1]}[2]} with the Hubble radius as the IR cut-off. However, as pointed out in Ref. [3]}, the resultant equation of state is greater than \(-1/3\)  and thus the vacuum energy fails to accelerate the cosmic expansion, if we simply take the Hubble radius \(L=1/H\)  as the IR cut-off. Later in the same year, by adopting the future event horizon as the IR cut-off, an accelerated expanding solution in the Friedman equation was eventually obtained in Ref.[4]}. Interestingly, the cosmic coincidence problem can also be resolved by inflation in this scenario, provided the minimal number of inflationary e-foldings. Since then, the holographic dark energy has drawn a lot of attention and has been widely studied, see Ref. [5]} for a comprehensive review on the topic. In passing, I shall mention that it was pointed out very recently that the holographic dark energy model may alleviate the Hubble tension problem [6]}.
